Distance between 2 atoms in a crystal

1. Jun 9, 2013

Nemo's

1. The problem statement, all variables and given/known data

Given a crystal (cube) with regularly arranged atoms (Total 27 atoms)
The mass of each atom is 3.5*10^-25. The density of the crystal is 9.2*10^3
What is the shortest distance between the centres of two adjacent atoms?

2. Relevant equations

density = mass / volume

3. The attempt at a solution

Volume= (27*3.5*10^-25)/(9.2*10^3)=1.03*10^-27
Length(L)=1*10-9
Distance between two atoms is L/2=5.04*10^-10

2. Jun 9, 2013

barryj

do you thinkthis is the correct answer?

3. Jun 9, 2013

4. Jun 9, 2013

barryj

L is correct. Should you really be dividing by 2?

5. Jun 9, 2013

Nemo's

Sorry the correct answer should be 3.4*10^-10
Should I divide by 3 then ? Why ?

6. Jun 9, 2013

barryj

What you probably did was to assume the volume of 27 atoms had an atom at every corner and one between. But if you put this volume next to another, the atoms on the edges would be to close. In fact, the distance should be 3.

7. Jun 11, 2013

Nemo's

So the atoms on the edges would be closer than others and that's the required "shortest distance"?
I just can't really imagine what it looks like

8. Jun 11, 2013

barryj

Maybe I wasn't clear. Put the atoms in a uniform rectangular three dimensional grid. My attachment shows the top view. Notice the volume is (3d)^3

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9. Jun 11, 2013

haruspex

The difficulty is, what does volume (and therefore density) mean when applied to a crystal consisting of only 27 atoms? It does not say that the density given is for arbitrarily large chunks of this material - it is for specifically this crystal of 27 atoms. So I tend to agree with Nemo's answer.

10. Jun 11, 2013

barryj

Good point, I guess whoever stated the "correct answer" thought it was for a large chunk.